Which of the following numbers is a multiple of 2? ${45,47,67,78,95}$
Answer: The multiples of $2$ are $2$ $4$ $6$ $8$ ..... In general, any number that leaves no remainder when divided by $2$ is considered a multiple of $2$ We can start by dividing each of our answer choices by $2$ $45 \div 2 = 22\text{ R }1$ $47 \div 2 = 23\text{ R }1$ $67 \div 2 = 33\text{ R }1$ $78 \div 2 = 39$ $95 \div 2 = 47\text{ R }1$ The only answer choice that leaves no remainder after the division is $78$ $ 39$ $2$ $78$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $2$ are contained within the prime factors of $78$ $78 = 2\times3\times13 2 = 2$ Therefore the only multiple of $2$ out of our choices is $78$. We can say that $78$ is divisible by $2$.